Geodesic spheres — 3 articles found.

Bounded Circles on a Complex Hyperbolic Space are Expressed by Trajectories on Geodesic Spheres

C. R. Math. Rep. Acad. Sci. Canada Vol. 46 (1) 2024, pp. 1–10
Vol.46 (1) 2024
Yusei Aoki; Toshiaki Adachi Details
(Received: 2023-12-06 , Revised: 2023-12-27 )
(Received: 2023-12-06 , Revised: 2023-12-27 )

Yusei Aoki , Division of Mathematics and Mathematical Science, Nagoya Institute of Technology, Nagoya 466-8555, Japan; e-mail: yusei11291@outlook.jp

Toshiaki Adachi , Department of Mathematics, Nagoya Institute of Technology, Nagoya 466-8555, Japan; e-mail: adachi@nitech.ac.jp

Abstract/Résumé:

We take a bounded circle on a complex hyperbolic space. We show that if it has complex torsion either \(\pm 1\) or \(0\) then it is expressed by a geodesic on some geodesic sphere, and show that if it has complex torsion \(\tau\) with \(0 < |\tau| < 1\) then it is uniquely expressed by a non-geodesic trajectory on a geodesic sphere up to congruency.

Nous prenous un cercle borné en l’espace hyperbolique complexe. Nous montrons que il est exprimé par une géodésique sur une sphère géodésique si sa torsion complexe est \(0\) ou \(\pm 1\), et montrons que il est uniquement exprimé par une trajectoire sur une sphère géodésique qui n’est pas une géodésique si sa torsion complexe est \(0 < |\tau| < 1\).

Keywords: Geodesic spheres, circles, complex torsions, congruent, extrinsic shapes

AMS Subject Classification: Hermitian and K_õhlerian structures, Sub-Riemannian geometry, Geodesics 53B35, 53C17, 53C22

PDF(click to download): Bounded Circles on a Complex Hyperbolic Space are Expressed by Trajectories on Geodesic Spheres

Nonnegatively Curved Geodesic Spheres in a Complex Hyperbolic Space

C. R. Math. Rep. Acad. Sci. Canada Vol. 35 (3) 2013, pp. 114–120
Vol.35 (3) 2013
Sadahiro Maeda Details
(Received: 2013-05-01 , Revised: 2013-09-15 )
(Received: 2013-05-01 , Revised: 2013-09-15 )

Sadahiro Maeda, Department of Mathematics, Saga University, Saga, 840-8502, Japan; e-mail: smaeda@ms.saga- u.ac.jp

Abstract/Résumé:

We characterize geodesic spheres with sufficiently small radii in a complex hyperbolic space by using their geometric properties. These geodesic spheres are the only examples of hypersurfaces of type (A) having nonnegative sectional curvature in this ambient space.

Nous caractérisons les sphères géodésiques de rayon suffisamment petit dans un espace hyperbolique complexe en utilisant leurs propriétés géométriques. Ces sphères géodésiques sont les seuls exemples d’hypersurfaces de type (A) qui ont courbure non-negative dans cet espace ambiant.

Keywords: Geodesic spheres, circles, complex hyperbolic spaces, contact form, exterior differentiation, geodesics, hypersurfaces of type (A), sectional curvatures

AMS Subject Classification: Local submanifolds 53B25

PDF(click to download): Nonnegatively Curved Geodesic Spheres in a Complex Hyperbolic Space

Characterization of complex space forms in terms of characteristic vector fields on geodesic spheres

C. R. Math. Rep. Acad. Sci. Canada Vol. 28 (4) 2006, pp. 114–120
Vol.28 (4) 2006
Sadahiro Maeda Details
(Received: 2006-05-30 )
(Received: 2006-05-30 )

Sadahiro Maeda, Department of Mathematics, Shimane University, Matsue 690-8504, Japan; email: smaeda@riko.shimane-u.ac.jp

Abstract/Résumé:

Investigating geometric properties of characteristic vector fields on geodesic spheres in a complex space form, we characterize complex space forms in the class of Kähler manifolds.

En étudiant des propriétés géométriques de champs de vecteurs caractéristiques sur des sphères géodésiques dans un espace complexe à courbure constante, on caractérise ces espaces dans la classe des variétés kähleriennes.

Keywords: Geodesic spheres, Kahler manifolds, Killing vector fields, characteristic fields, complex space forms, totally geodesic complex curves

AMS Subject Classification: Local submanifolds 53B25

PDF(click to download): Characterization of complex space forms in terms of characteristic vector fields on geodesic spheres

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